> Category Theory always felt almost mechanical to me. Lots of definitions and rules for assembling diagrams and such, but then what.
Category Theory is more about getting (as one of my professors put it) "a God's-eye view of mathematics". What I have found to be the most deep and useful is the way it provides concrete definitions which unite constructions that mathematicians were already calling the same thing (e.g. products, co-products). It is also absolutely amazing at showing links between different (seemingly unrelated) parts of mathematics. In this way, it forms a sort of lingua-franca for mathematics. This math StackExchange answer[1] gives some really good concrete examples.
If you want a book which gives a lot of more concrete results along with category theory, you should try Algebra: Chapter 0. It is more focused on abstract algebra, but it does it all from a categorical perspective while not assuming you know one iota of category theory (at the start).
Category Theory is more about getting (as one of my professors put it) "a God's-eye view of mathematics". What I have found to be the most deep and useful is the way it provides concrete definitions which unite constructions that mathematicians were already calling the same thing (e.g. products, co-products). It is also absolutely amazing at showing links between different (seemingly unrelated) parts of mathematics. In this way, it forms a sort of lingua-franca for mathematics. This math StackExchange answer[1] gives some really good concrete examples.
If you want a book which gives a lot of more concrete results along with category theory, you should try Algebra: Chapter 0. It is more focused on abstract algebra, but it does it all from a categorical perspective while not assuming you know one iota of category theory (at the start).
[1]: http://math.stackexchange.com/questions/312605/what-is-categ...